Question 55: Ray Optics

Question

The image of an object, formed by a plano-convex lens at a distance of 8 m behind the lens, is real and is
one-third the size of the object. The wavelength of light inside the lens is $${2 \over 3}$$ times the wavelength in free space. The radius of the curved surface of the lens is

Accepted Answer

The speed of light in a medium is given by the equation :
$$ \frac{C}{V}=\frac{\lambda_0}{\lambda}=\mu $$
Where :
V
is the velocity of light in the medium
ÃÂ»
is the wavelength of light in the medium
ÃÂ»
0
is the wavelength in free space
ÃÂ¼
is the refractive index of the medium
Given :
$$ \lambda=\frac{2}{3} \lambda_0 $$
Using the given data :
$$\begin{aligned} u & = -24 	ext{ m},\\ h_i & = \frac{1}{3}h_0\end{aligned}$$
To find the magnification (
m
) :
$$ m = \frac{h_i}{h_0} = \frac{1}{3} = \frac{v}{u} $$
Hence,
$$ v = \frac{u}{3} $$
Given :
$$ v = 8 	ext{ m},\ u = -24 	ext{ m} $$
Applying the lens formula :
$$ \frac{1}{v} - \frac{1}{u} = \frac{1}{f} = (\mu - 1)\left(\frac{1}{R_1} - \frac{1}{R_2}ight) $$
Since the plane surface has an infinite radius :
$$ \frac{1}{\infty} = 0 $$
Therefore :
$$\frac{1}{8} - \frac{1}{-24} = (1.5 - 1)\left(\frac{1}{R} - 0ight)$$
$$\Rightarrow \frac{1}{6} = \frac{0.5}{R}$$
Solving for
R
:
$$ \Rightarrow R = 3 	ext{ m} $$

Answer

1 m

Answer

2 m

Answer

3 m

Answer

6 m

Ray Optics

The image of an object, formed by a plano-convex lens at a distance of 8 m behind the lens, is real and is one-third the size of the object. The wavelength of light inside the lens is ${2 \over 3}$ times the wavelength in free space. The radius of the curved surface of the lens is

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